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Minimax optimal control problems. Numerical analysis of the finite horizoncase

Published online by Cambridge University Press:  15 August 2002

Silvia C. Di Marco  and
Roberto L.V. González
Silvia C. Di Marco
Affiliation:
CONICET – Inst. Beppo Levi, Dpto. Matemática, FCEIA, Universidad Nacional de Rosario, Rosario, Argentine.
Roberto L.V. González
Affiliation:
CONICET – Inst. Beppo Levi, Dpto. Matemática, FCEIA, Universidad Nacional de Rosario, Rosario, Argentine.
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Abstract

In this paper we consider the numerical computation of the optimal costfunction associated to the problem that consists in finding the minimum ofthe maximum of a scalar functional on a trajectory. We present anapproximation method for the numerical solution which employs bothdiscretization on time and on spatial variables. In this way, we obtain afully discrete problem that has unique solution. We give an optimal estimatefor the error between the approximated solution and the optimal costfunction of the original problem. Also, numerical examples are presented.

Keywords

minimax problemsoptimal cost functiondiscretemaximum principlefully discrete solution.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 33 , Issue 1 , January 1999 , pp. 23 - 54
Copyright
© EDP Sciences, SMAI, 1999

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